Parallel Electrical Circuits

The resistors that its terminals is connected to the reciprocal same points is called parallel resistors.

In the figure, It is seen a circuit that have only parallel resistors.

The left side of all of three of these resistors are merge on the point A2.

The left pole of all three of these resistors are merge on the point A2. Also, The right pole of all three of these resistors are merge on the point B1.

Points A1 and A2 are the same points. Also, Points B1 and B2 are the same points.

Because of the current is divided to the branches, the circuits that have parallel resistors is also called current divider circuits.

The Voltage Drop In Parallel Connected Resistors

The voltage is equal across in each of the parallel resistors. If there is no a resistor connected in series in the circuit, the voltage across the each of resistors is equal to the supply voltage .

Example, In the circuit in the figure above, the voltage across each of the resistors is,

VR1 = 30 V

VR2 = 30 V

VR3 = 30 V

Current In Parallel Connected Circuits

In the parallel circuits, the main current is divided into the branches . If the value of the resistor in a parallel arm and the voltage across resistor are known, the current in that arm can be found from term of V/R.

If the voltage and current are not known in any branch, then the equivalent current of the circuit is found and the calculations are does according to this.

In the circuit in the figure above has only parallel resistors. In this circuit, the voltages across all resistors are equal, and these voltage of each are equal to the supply source.

IR1 =

30

10

IR1 = 3 A

IR2 =

30

15

IR2 = 2 A

IR3 =

30

6

IR3 = 5 A

The sum of these currents gives the current that taken from source.

Is = I1 + I2 + I3

Is = 3 + 2 + 5

Is = 10 A

If there are two parallel resistors, the current flow through each of resistors can found as follows.

I1 =

Is•R2

R1 + R2

I2 =

Is•R2

R1 + R2

The Equivalent Resistance Of Parallel Connected Resistors

If numbers of the parallel resistors is n, the equivalent resistance of these resistors is found as follows.

1

=

1

+

1

+ ...+

1

Rn

R2

R1

Rs

Let we calculate the equivalent resistance of electrical circuit in the figure above.

1

=

1

+

1

+

1

16

15

10

Rs

1

=

3

+

2

+

5

30

30

30

Rs

Rs =

30

10

Rs = 3 Ω

We can found the equivalent current using the equivalent resistance.

Is =

V

Rs

Is =

30

3

Is = 10 A

This result be compatible with the result which we calculate above.

If the value of each of resistors are equal, the equivalent resistance can be found by dividing the value of the resistance in any branch by the number of branches.